Energy levels of QED in a Euclidean formulation

Hydrogen-like energy levels of scalar and spinor QED are calculated using a Euclidean functional approach. The matter field is integrated over. Stationary points of the resulting effective action already yield a hydrogen like level structure for the energy. There is an interesting difference between the scalar and the spinor case. Whereas for spinors the conventional results are reproduced, the calculation for scalars yields a fine structure which is opposite in sign to the conventional one and has no critical singularity at Zα=1/2. The crucial structural difference between the two cases is that, for scalars, minima for the gauge invariant energy are not extrema of the action, even for time independent fields.     

Scalar lattice gauge theory

Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed from scalars. For suitable parameters scalar lattice gauge theories lead to confinement, with all continuum observables identical to usual lattice gauge theories. These models or their fermionic counterpart may be helpful for a realization of gauge theories by ultracold atoms. We conclude that the gauge bosons of the standard model of particle physics can arise as collective fields within models formulated for other “fundamental” degrees of freedom.     

The vortex free energy in the screening phase of the Z(2) Higgs model

The vortex free energy was proposed to distinguish between the confinement and the Higgs phase (in the sense of 't Hooft) in lattice gauge theory, when matter fields are present that transform according to an arbitrary representation of the gauge group. In this paper I consider the Z(2) Higgs model and calculate the vortex free energy in the screening part of the confining/screening phase of Fradkin and Shenker. The result does not agree with the expected behavior that corresponds to the structure of the phase diagram. Therefore the vortex free energy is no longer a good indicator for confinement when matter fields transform non-trivially under the center of the gauge group (such as Z(2) Higgs scalars).     

Dirac Sigma Models

We introduce a new topological sigma model, whose fields are bundle maps from the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an exact Courant algebroid over a target manifold. It generalizes simultaneously the (twisted) Poisson sigma model as well as the G/G-WZW model. The equations of motion are satisfied, iff the corresponding classical field is a Lie algebroid morphism. The Dirac Sigma Model has an inherently topological part as well as a kinetic term which uses a metric on worldsheet and target. The latter contribution serves as a kind of regulator for the theory, while at least classically the gauge invariant content turns out to be independent of any additional structure. In the (twisted) Poisson case one may drop the kinetic term altogether, obtaining the WZ-Poisson sigma model; in general, however, it is compulsory for establishing the morphism property.     

The supersymmetric Higgs mechanism—Quartet decoupling and nondoubled Goldstone bosons

A complete quantum field theoretic analysis of the supersymmetric Higgs mechanism is presented, in the general case where the Goldstone bosons may be either doubled or nondoubled. If gauge fields are coupled to nondoubled Goldstone bosons, it is found that supersymmetry is spontaneously broken not just by the masses but also by the spins of the physical particles. The spectrum reveals no supersymmetry multiplet structure. The decoupling of unphysical degrees of freedom is carefully discussed, and the quartet decoupling mechanism for gauged Goldstone bosons is extended to supersymmetry theories. The results are illustrated with an SU(2) × U(1) model.     

A METHOD ON DERIVATION OF GAUGE FIELDS

Usually the study of gauge field is based on the wave function. By discussing thebehaviour of Dirac particles in gravitation, one has a famous difficulty, that is, thewave functions appear as scalars under general coordinate transformations. In thispaper, a method is suggested to constitute the gauge fields directly from algebraicstructures, Lie algebra and Jordan algebra. We introduce a concept called represen-tation group of algebras, the transformations, of wave function are connected with therepresentation group. The global and local representation groups are connected withglobal and local transformations of wave function respectively. According to thismethod we find that it is equivalent to the usual one for all of the problems concernedwith internal freedom as Yang-Mills field etc. For spinors, one can introduce gravi-tation by changing the algebraic structure, one find that the vierbein is unneccessaryand the wave functions transform as spinors corresponding to Dirac theory. Somerelated problems are also discussed.     

The goldstone fields of interacting higher spin field theory in AdS(4)

A higher spin field theory on AdS(4) possesses a conformal theory on the boundary R(3) which can be identified with the critical O(N) sigma model of O(N) invariant fields only. The notions of quasiprimary and secondary fields can be carried over to the AdS theory. If de Donder’s gauge is applied, the traceless part of the higher spin field on AdS(4) is quasiprimary and the Goldstone fields are quasiprimary fields to leading order too. Those fields corresponding to the Goldstone fields in the critical O(N) sigma model are odd-rank symmetric tensor currents which vanish in the free-field limit. The text was submitted by the author in English.     

Stochastic field theory for a dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four-dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effective supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.     

Baryon-antibaryon asymmetry in a model with domain structure and soft CP violation

We consider a model with an abelian gauge symmetry, a Higgs potential involving two scalar fields, and two spinor fields coupled to the scalars through Yukawa couplings. The model accomodates soft violation of charge conjugation, and a domain structure of the universe with two different types of domains, which have identical energy but are governed by different effective lagrangians. The effective lagrangian has complex c-number coefficients that become parts of effective coupling constants, and these are different in the two kinds of domains. In spite of that fact the model neither predicts any domain-dependent effects, nor any particle-antiparticle asymmetries within domains.     

The background field method and the linearization problem for Poisson manifolds

The background field method (BFM) for the Poisson sigma model (PSM) is studied as an example of the application of the BFM technique to open gauge algebras. The relationship with Seiberg–Witten maps arising in non-commutative gauge theories is clarified. It is shown that the implementation of the BFM for the PSM in the Batalin–Vilkovisky formalism is equivalent to the solution of a generalized linearization problem (in the formal sense) for Poisson structures in the presence of gauge fields. Sufficient conditions for the existence of a solution and a constructive method to derive it are presented.     

Towards gauge unified,supersymmetric hidden strong dynamics

We consider a class of models with extra complex scalars that are charged under both the Standard Model and a hidden strongly coupled S U(N)h gauge sector and discuss the seenarios in which the new scalars are identified as the messenger fields that mediate the spontaneously broken supersymmetries from the hidden sector to the visible sector.The new scalars are embedded into 5-plets and 10-plets of an S(/(5)v gauge group that potentially unifies the Standard Model gauge groups.The Higgs bosons remain as elementary particles.In the supersymmetrized version of this class of models,vector-like fermions whose left-handed components are superpartners of the new scalars are introduced.Owing to the hidden strong force,the new low-energy scalars hadronize before decaying and thus evade the common direct searches of the supersymmetric squarks.This can be seen as a gauge mediation seenario with the scalar messenger fields forming low-energy bound states.We also discuss the possibility that in the tower of bound states formed under hidden strong dynamics(of at least the TeV scale),there exist a dark matter candidate and the collider signatures(e.g.diphoton,diboson,or dijet)of models that may show up in the near future.     

Four-dimensional heterotic string models with third-integral twists

The massless string states are constructed for a four-dimensional heterotic string model with the U(5) gauge group in the untwisted sector. The complete observable gauge group, quark and lepton generations, Higgs scalar structure, quark and lepton mass matrix, couplings to colour triplet scalars, and gauge symmetry breaking are studied for this model.     

BLG and M5

We discuss the interpretation of the three-dimensional N = 8 superconformal Chern-Simons-matter theory with the gauge group of volume preserving diffeomorphisms as a model describing a six-dimensional self-dual gauge field coupled to scalars and spinors and its possible relation to the M5-brane     

Loop variables and gauge invariant exact renormalization group equations for (open) string theory

An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non-zero mass is essential for this. This is reminiscent of Abelian Born–Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.     

Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism

We consider noncommutative gauge theory defined by means of Seiberg–Witten maps for an arbitrary semisimple gauge group. We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters θ. We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group. We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg–Witten maps that are linear in the matter fields. Surprisingly, it turns out that the UV divergent parts of the matter contributions are proportional to the noncommutative Yang–Mills action where traces are taken over the representation of the matter fields; this result supports the need to include such traces in the classical action of the gauge sector of the noncommutative theory.     

Four-dimensional heterotic string models with SU(5) and SO(10) grand unification

The gauge group, quark and lepton generations, Higgs scalar structure, couplings of quarks and leptons to Higgs scalars and to colour triplet scalars, and the gauge symmetry breaking are studied for a class of four-dimensional heterotic string models whose boundary conditions include third-integral twists.     

Skew-symmetric tensor gauge field theory dynamically realized in the QCD U(1) channel

It is shown that, in order for the U(1) Goldstone boson to decouple from the physical sector, a third rank skew-symmetric tensor gauge field theory has to be realized dynamically by asymptotic fields of bound states in QCD. The abelian-like gauge invariance of this tensor gauge theory is just a realization of the original QCD gauge (BRS) invariance which hence assures the decoupling of all the bound-state modes by the “quarlet mechanism”. A general procedure for fixing gauges in such types of skew-symmetric tensor gauge theories is also presented.     

Exotic Yang–Mills Dilaton Gauge Theories

An exotic class of nonlinear p-form non-Abelian gauge theories is studied, arising from the most general allowed covariant deformation of linear Abelian gauge theory for a set of massless 1-form fields and 2-form fields in four dimensions. These theories combine a Chapline–Manton type coupling of the 1-forms and 2-forms, along with a Yang–Mills coupling of the 1-forms, a Freedman–Townsend coupling of the 2-forms, and an extended Freedman–Townsend type coupling between the 1-forms and 2-forms. It is shown that the resulting theories have a geometrically interesting dual formulation that is equivalent to an exotic Yang–Mills dilaton theory involving a nonlinear sigma field. In particular, the nonlinear sigma field couples to the Yang–Mills 1-form field through a generalized Chern class 4-form term.     

Triviality pursuit: Can elementary scalar particles exist?

Great effort is presently being expended in the search for elementary scalar “Higgs” particles. These particles have yet to be observed. The primary justification for this search is the theoretically elegant Higgs-Kibble mechanism, in which the interactions of elemetary scalars are used to generate gauge boson masses in a quantum field theory. However, strong evidence suggests that at least a pure φ⁴ scalar field theory is trivial or noninteracting. Should this triviality persist in more complicated systems such as the standard model of the weak interaction, the motivation for looking for Higgs particles would be seriously undermined. Alternatively, the presence of gauge and fermion fields can rescue a pure scalar theory from triviality. Phenomenological constraints (such as a bounded or even predictable Higgs mass) may then be implied. In this report the evidence for triviality in various field theories is reviewed, and the implications for high energy physics are discussed.     

Effective actions for scalars and spinors in a general Robertson-Walker universe

The effective actions for massless scalars and spinors in a four-dimensional conformally flat spacetime are found. The cross term due to interaction with external gauge field is integrable and induces asymptotic freedom for the gauge coupling constant.